Canadian Computing Competition: 2011 Stage 2, Day 2, Problem 1

Alice and Bob own a huge company. This company was losing money consistently over the last 30 years, since its owners spent too much time playing games with mathematicians. Alice and Bob decide to make a change.

Alice and Bob start by giving unique employee IDs to each of the ~n~ employees ~(1 \le n \le 100\,000)~, where each ID ~I~ is in the range ~(1 \le I \le 100\,000)~.

Then, Alice and Bob give unique ranks to each employee. Each rank ~R~ is an integer such that ~1 \le R \le 10\,000\,000~. After this, they plan to reorganize the company, by making sure that the employees satisfy the following conditions:

1. There is exactly one director, who has no supervisor;
2. Except for the director, each employee has a supervisor, and this supervisor has a smaller employee ID and a higher rank (the value of rank is smaller); and
3. Each employee can supervise at most 2 people.

Alice and Bob are eager to know whether their company can be reorganized successfully.

Input Specification

The input is a total of ~2~ lines. The first line contains ~n~ ~(1 \le n \le 100\,000)~, indicating the number of employees. The next line contains ~n~ distinct integers ~R~ ~(1 \le R \le 10\,000\,000)~, where the ~i~th integer indicates the rank of the employee with ID ~i~.

Output Specification

Output YES if the company can be reorganized successfully; output NO otherwise.

Sample Input 1

6
1 6 5 2 3 4

Sample Output 1

NO

Explanation for Sample Output 1

Employee with rank 1 has employee ID 1, and thus, must be the supervisor. Employees 2 and 3 (with ranks 6 and 5) can only be supervised by employee 1 (with rank 1). However, no other employee (4, 5 or 6) can be supervised by employee 2 or employee 3, since ranks of supervisors must be smaller than the employees they supervise.

Sample Input 2

6
1 6 2 3 4 5

Sample Output 2

YES

Explanation for Sample Output 2

Employee 1 (rank 1) supervises both employee 2 (rank 6) and employee 3 (rank 2).

Employee 3 (rank 2) supervises employee 4 (rank 3) and employee 5 (rank 4).

Employee 4 (rank 3) supervises employee 6 (rank 5).